I would like to approximate (or calculate) the below sum.
$$ \frac {1} {{2 N \choose M}} \, \sum_{k = 1}^{N / 2} \frac {2^{2 k}} {2 k} \, {N \choose 2 k} \, {N - 2 k \choose \frac {M - 2 k} {2}} $$
Do you know any methods I could use? Thanks
2026-04-12 03:10:26.1775963426
Approximation of a sum
87 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in SUMMATION
- Computing:$\sum_{n=0}^\infty\frac{3^n}{n!(n+3)}$
- Prove that $1+{1\over 1+{1\over 1+{1\over 1+{1\over 1+...}}}}=\sqrt{1+\sqrt{1+\sqrt{1+\sqrt{1+...}}}}$
- Fourier series. Find the sum $\sum_{n=1}^\infty \frac{(-1)^{n+1}}{2n+1}$
- Sigma (sum) Problem
- How to prove the inequality $\frac{1}{n}+\frac{1}{n+1}+\cdots+\frac{1}{2n-1}\geq \log (2)$?
- Double-exponential sum (maybe it telescopes?)
- Simplify $\prod_{k=1}^{l} \sum_{r=d}^m {{m}\choose{r}} \left(N-k \right)^{r} k^{m-r+1}$
- Sum of two martingales
- How can we prove that $e^{-jωn}$ converges at $0$ while n -> infinity?
- Interesting inequalities
Related Questions in BINOMIAL-COEFFICIENTS
- Newton binomial expansion
- Justify an approximation of $\sum_{n=1}^\infty G_n/\binom{\frac{n}{2}+\frac{1}{2}}{\frac{n}{2}}$, where $G_n$ denotes the Gregory coefficients
- Solving an equation involving binomial coefficients
- Asymptotics for partial sum of product of binomial coefficients
- What is wrong with this proof about a sum of binomial coefficients?
- Find sum of nasty series containing Binomial Coefficients
- Alternating Binomial Series Summation.
- $x+\frac{1}{x}$ is an integer
- Finding value of $S-T$ in $2$ binomial sum.
- how to reduce $(1-\alpha)^{T-i}$ into a sum
Related Questions in APPROXIMATION
- Does approximation usually exclude equality?
- Approximate spline equation with Wolfram Mathematica
- Solving Equation with Euler's Number
- Approximate derivative in midpoint rule error with notation of Big O
- An inequality involving $\int_0^{\frac{\pi}{2}}\sqrt{\sin x}\:dx $
- On the rate of convergence of the central limit theorem
- Is there any exponential function that can approximate $\frac{1}{x}$?
- Gamma distribution to normal approximation
- Product and Quotient Rule proof using linearisation
- Best approximation of a function out of a closed subset
Related Questions in FACTORIAL
- How is $\frac{\left(2\left(n+1\right)\right)!}{\left(n+1\right)!}\cdot \frac{n!}{\left(2n\right)!}$ simplified like that?
- Remainder of $22!$ upon division with $23$?
- What is the name of this expression?
- How to compute $\left(\frac{n-1}{2}\right)!\pmod{n}$ fast?
- Proving $\sum_{k=1}^n kk!=(n+1)!−1$
- How do we know the Gamma function Γ(n) is ((n-1)!)?
- Approximate value of $15!$
- Limit of a Sequence involving factorials
- How to understand intuitively the fact that $\log(n!) = n\log(n) - n + O(\log(n))$?
- Deriving the fact that the approximation $\log(n!) \approx n\log(n) - n + \frac{1}{2}\log(2\pi n)$ is $O(1/n)$.
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?